Right now it's the Mariners. Until this year, the longest streak was held by the Royals and the second-longest the Blue Jays...but the Royals are in the Series this year and it is what it is.
Deleted previous one. Lakers did not make the playoffs in the 2004-2005 season. The real answer is the San Antonio Spurs, who have made the playoffs every year since 1998.
Through the 2008 season, that is the Washington Nationals/Montreal Expos franchise whose last (and only) playoff appearance was in 1981.
Patriots won 21 games straight from 2003-2004 (including playoffs) it's the longest streak in modern day football
I can only speak for North American professional sports and that would be the Boston Bruins of the NHL who made the playoffs for 29 consecutive seasons from 1967-68 through 1995-96.
The Buffalo Bills were last in the playoffs during the 1999 season.
Longest streak goes to BYU Do not currently know who has the longest current streak
AC Roma is the team in Serie A that has had the longest winning streak of 10 games in the 2013 2014 season.